I hate to break it to you, but ALL of your Switch save data is stored locally now. Save files are all stored, regardless of the game, on your Switch itself, not on the cartridges. If your Switch randomly breaks, you're going to lose everything anyway unless you have the Online subscription and Cloud Saves enabled, but even then it's not going to save everything. I think the two high profile titles not supported by it are Splatoon 2 and Pokemon Let's Go, though there may be more.
Whether Animal Crossing will be supported by it remains to be seen, but I'm going to imagine it won't for the same reasons as Splatoon and Pokemon: Duplication and rerolls.